Minimun is a relative quantity. This indicates the minimum variance among the estimators under consideration. This should not be confused with a Crammer–Rao lower bound. If any estimator attains this bound, then it is the best estimator.

These coefficients are estimated using the average life and magnitude of margins for APUs.

Note that the stamp of the event is assumed to be known. In the case of line maintenance action, the event time stamp is deterministic; however, this is random for an abrupt fault. We assume the availability of external observers to detect such events.

Prognostic health monitoring is an important element of condition-based maintenance and logistics support. The accuracy of prediction and the associated confidence in prediction greatly influence overall performance and subsequent actions either for maintenance or logistics support. Accuracy of prognosis is directly dependent on how closely one can capture the system and component interactions. Traditionally, such models assume a constant and univariate prognostic formulation—that is, components degrade at a constant rate and are independent of each other. Our objective in this paper is to model the degrading system as a collection of prognostic states (health vectors) that evolve continuously over time. The proposed model includes an age dependent deterioration distribution, component interactions, as well as effects of discrete events arising from line maintenance actions and/or abrupt faults. Mathematically, the proposed model can be summarized as a continuously evolving dynamic model, driven by non-Gaussian input and switches according to the discrete events in the system. We develop this model for aircraft auxiliary power units, but it can be generalized to other progressive deteriorating systems. The system identification and recursive state estimation scheme for the developed non-Gaussian model under a partially specified distribution framework has been deduced. The diagnostic/prognostic capabilities of our model and algorithms have been demonstrated using simulated and field data.

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